The pulmonary airway, arterial, venous and capillary networks are vast complex branching and converging systems that are mechanically coupled to the surrounding lung tissue. Early studies that examined vascular or airway geometry relied on measurements from casts, but medical imaging now enables measurement of the lung in vivo, at controlled lung volumes. The high-quality data that imaging provides have prompted development of increasingly sophisticated models of the geometry of the airway and pulmonary vascular trees. The accurate spatial relationships between airway, vessel and tissue in these imaging-derived models are necessary for computational analysis that aims to elucidate regional airway-vessel-tissue interactions. Predictions of blood flow through multiscale imaging-derived models of the pulmonary arteries and capillary bed reveal geometry-dependent patterns of perfusion in response to gravity and lung orientation that cannot be predicted with simplified, summary representations of the pulmonary transport trees. Validation of such predictions against measures from functional imaging holds significant potential for explaining and differentiating normal and disease-related heterogeneity in regional blood flow calculated using perfusion imaging.